Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

Abstract

We consider Hermitian random band matrices H in d geqslant 1 dimensions. The matrix elements H_{xy}, indexed by x, y in varLambda subset mathbb {Z}^d, are independent, uniformly distributed random variable if |x-y| is less than the band width W, and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |varLambda | of the matrix.